1. Field of the Invention
The invention relates to optical communications, and, in particular, to optical buffers employing four-wave mixing.
2. Description of the Related Art
All-optical communication systems have the potential to transmit information at bit rates higher than 10 Gb/s. Such systems employ tunable optical buffers, i.e., delay elements, with bit-level control, to implement bit-interleaved or packet-interleaved multiplexing, and to prevent conflicts among different bit streams at optical switches. M. Burzio, P. Cinato, R. Finotti, P. Gambini, M. Puleo, E. Vezzoni, and L. Zucchelli, “Optical cell synchronisation in an ATM optical switch,” Proc. ECOC 1994, pp. 581-584, the teachings of which are incorporated herein by reference, describe an optical buffer employing opto-electronic frequency conversion. J. E. Sharping, Y. Okawachi, J. van Howe, C. Xu, Y. Wang, A. E. Willner, and A. L. Gaeta, “All-optical, wavelength and bandwidth preserving, pulse delay based on parametric wave-length conversion and dispersion,” Opt. Express 13, 7872-7877 (2005), the teachings of which are incorporated herein by reference, describe an optical buffer employing modulation interaction (MI), a particular type of four-wave mixing (FWM), in a fiber.
Four-wave mixing is a parametric interaction in which two input photons are destroyed and two different, output photons are created. FIG. 1 illustrates three different types of FWM: modulation interaction (MI), phase conjugation (PC), and Bragg scattering (BS), which is also referred to as frequency conversion (FC). In FIG. 1, ω1+ represents the frequency of an input (data) signal having photons γ1+, ω1 represents the frequency of light from a first pump (P1) having photons γ1, ω2 represents the frequency of light from a second pump (P2) having photons γ2, and ω represents the frequency difference between the input signal and the first pump wave (i.e., ω=ω1+˜ω1, where the symbol “˜” means minus). In FIG. 1, input signal ω1+ is a sideband signal relative to pump signals ω1 and ω2, where ω1−, ω2−, and ω2+ represent the frequencies of the remaining three sideband signals, which are also referred to as idler signals (because they are usually generated by the FWM process). In conventional optoelectronics parlance, input signal ω1+ is referred to simply as a “signal,” pump signals ω1 and ω2 are referred to simply as “pumps,” and idler signals ω1−, ω2−, and ω2+ are referred to simply as “idlers.” Although pump signals are inputs in FWM processes, the term “input signal” as used in this specification will be understood to refer to a “signal” of conventional optoelectronics parlance and not to a “pump.”
In MI, a single pump wave ω1 interacts with the input signal ω1+ according to 2γ1→γ1−+γ1+, such that two pump photons 2γ1 are destroyed, and one signal photon γ1+ and one idler photon γ1− are created, where ω1−=(ω1˜ω). In PC, two pump waves ω1 and ω2 interact with the input signal ω1+ according to γ1+γ2→γ1++γ2−, such that two pump photons γ1 and γ2 are destroyed, and one signal photon γ1+ and one idler photon γ2− are created, where ω2−=(ω2˜ω). In BS, two pump waves ω1 and ω2 interact with the input signal ω1+ according to γ1++γ2→γ1+γ2+, such that one signal photon γ1+ and one pump photon γ2 are destroyed, and one pump photon γ1 and one idler photon γ2+ are created, where ω2+=(ω2+ω). The value of the zero-dispersion frequency (ZDF) of the fiber in which the parametric interaction occurs, relative to the pump and signal frequencies, determines which type or types of FWM occur within the fiber.
The MI-based optical buffering described by Sharping et al. is a three-step process. First, MI is used to generate an idler pulse (e.g., ω1−) that is the frequency converted (FC) image of the input signal pulse (e.g., ω1+). Second, the idler is sent through a dispersive medium, such as a fiber. Third, MI is again used, this time to generate an output idler with the same frequency as the input signal. Because of dispersion, the output idler is delayed by an amount that is proportional to the frequency difference (i.e., ω1+˜ω1−) between the signal and intermediate idler.
There are (at least) three reasons why MI-based optical buffers are poor choices for communication systems: (1) their ability to controllably vary the delays is limited, (2) they are not suitable for multiple-channel systems, e.g., wavelength-division-multiplexed (WDM) systems, and (3) they generate low-quality output idlers.
In principle, one can vary the idler delay by varying the frequency difference between the input signal and the idler. In practice, the extent to which one can do this in MI-based optical buffers is limited. Suppose that the signal frequency ω1+ is fixed. If one were to vary the pump frequency ω1+, one would vary the idler frequency ω1−=2ω1˜ω1+. However, one would also vary the MI gain, which depends sensitively on the difference between the pump frequency and the ZDF of the fiber. For typical parameters, the constraint of nearly constant gain limits the pump and idler wavelengths to tuning ranges of a few nm.
Because the idler frequency ω1− equals 2ω1˜ω1+, the input signal-idler frequency difference ω1+˜ω1− equals 2(ω1+˜ω1), which depends on the signal frequency ω1+. As a result, signals in different channels experience different frequency shifts and, hence, different time delays. Hence, MI buffers are not suitable for use in WDM systems.
In many parametric devices, the pump powers exceed the stimulated Brillouin scattering (SBS) threshold by a wide margin. To circumvent SBS, pumps are phase-modulated to broaden their spectra and reduce the powers of their spectral component below the SBS threshold. Let the pump frequency be ω1+δω1, where ω1 is the average pump frequency, which is constant, and δω1 is the slowly varying perturbation to the pump frequency associated with phase modulation. Then, the idler frequency ω1− equals 2(ω1+δω1)˜ω1+. The MI idler inherits twice the phase modulation of the pump, and the dispersive fiber converts phase modulation into amplitude modulation. As a result, MI buffers generate low-quality output idlers.
MI amplifies the signal and generates a strong idler. However, with amplification comes noise. The addition of noise photons to a classical (i.e., many-photon) signal would not perturb the signal significantly and, hence, would not prevent the use of an MI buffer in a classical communication system. However, the addition of noise photons would perturb significantly the state of a quantal (i.e., few-photon) signal. Hence, MI buffers are not suitable for use in quantal communication systems.